Geodesic
Continuous branches of multivalued mappings with nonconvex right side
Sbornik. Mathematics, Tome 48 (1984) no. 2, pp. 339-348 
A. V. Bogatyrev. Continuous branches of multivalued mappings with nonconvex right side. Sbornik. Mathematics, Tome 48 (1984) no. 2, pp. 339-348. http://geodesic.mathdoc.fr/item/SM_1984_48_2_a3/
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     author = {A. V. Bogatyrev},
     title = {Continuous branches of multivalued mappings with nonconvex right side},
     journal = {Sbornik. Mathematics},
     pages = {339--348},
     year = {1984},
     volume = {48},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1984_48_2_a3/}
}
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This paper considers multivalued mappings which map a compact metric space into the space of nonempty closed subsets of $L_I^1$. A theorem asserting the existence of a continuous branch of such a mapping is proved. This theorem is analogous to a theorem of Michael. As corollaries, theorems on the existence of fixed points of multivalued mappings and on the existence of solutions of differential inclusions are proved. Bibliography: 13 titles.